Cryogenic performance of a compact high-effectiveness mesh-based counter-flow heat exchanger

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Introduction
Cryocooler-based remote cooling systems with a fluid circulation loop [1] aim to mechanically separate the cryocooler (cooling source) by some distance from the target to be cooled.Such systems provide an interesting option to deliver cooling power to installations, which operate in harsh environments in locations that cannot be reached easily [2].Remote cooling circuits would allow placing the cooling source further away from the test zone for experiments at CERN facilities such as CHARM [3], where radiation testing of equipment (e.g.bypass diodes) at low temperatures is performed.In this way, the irradiation of the cryocooler materials inside the coldhead can be avoided and its lifetime can be extended.Moreover, the remote cooling systems present a "dry" cooling solution that does not require local operation with liquid cryogens.This greatly simplifies installations from a safety perspective, allowing the replacement of more complex zero-boil-off cryostat options.The latter were previously used in liquefaction of cryogenic propellants in space exploration missions [4,5] and accelerator applications [6,7].Additionally, such systems can reduce the exported vibrations (compared to directly using a cryocooler as a cooling source) and even increase the overall cooling power delivered to the remote location [8].
This can serve as a great advantage in the applications, which are sensitive to mechanical and thermal disturbances, such as cooling of optical components of gravitational wave [9] and space infrared detectors.In the view of the latter application, the European Space Agency initiated the development of a 40 K Reverse Turbo-Brayton (RTB) cooler [10].
Effective and compact heat exchangers (HEX) are the backbone of remote cooling systems and RTB coolers, which are used for a range of on-ground and space applications [1,11,12].A defining factor for the HEX performance is its internal geometry.A variety of options exists [13] amongst which porous metal matrices stand out in terms of their compactness, i.e. high wetted area per volume and large heat transfer coefficients to the fluid flow [14].In particular, CFHEX designs, formed of stacked woven metal mesh screens, are predicted to have a very high effectiveness [1].This is possible as the mesh screens, which are stacked, have a non-homogeneous thermal conductivity [15]; their high in-plane conductivity allows to enhance heat transfer between the fluid flows while their low through-plane conductivity leads to a reduction in HEX axial conduction.Several mesh-based CFHEXs were accomplished previously [16,17] with the highest experimental NTU (number of transfer units, dimensionless performance metric) in the 8-15.7 range reported thus far.
This paper presents the results obtained in the experimental campaign to characterise the performance of a sized [1] and fabricated copper mesh-based CFHEX.Effectiveness values of 94.9 % (NTU = 18.6) for helium and 94.5 % (NTU = 17.2) for neon as operating fluids in the 50 K-290 K range have been achieved.The presented results include pressure drop and effectiveness values that were measured in the range of operating conditions (inlet pressures, mass flow rates, four different fluids) during warm (above 290 K) and cold (room temperature down to 46 K) tests.The findings are presented to the reader in three main parts.Firstly, the pressure drop measured during the warm tests is presented and the friction factor is extracted from this data.A new friction factor model for woven mesh is proposed and compared to existing literature models.This friction model is then used to predict the pressure drop at cold conditions and these predictions are compared to the experimental data.Secondly, the CFHEX static loss is measured and analysed.Thirdly, the CFHEX effectiveness is determined experimentally in both warm and cold testing conditions.The effectiveness predictions (which are obtained using a previously presented numerical model [1]) are correlated with the experimental data taking into account the conclusions drawn from the pressure drop and static loss measurements.Two parameters that strongly affect the CFHEX effectiveness are identified and analysed: the inner wall-to-mesh contact conductance and the mesh-to-fluid heat transfer.Finally, design improvements are proposed and the initial prediction of the cooling power of the remote cooling system [1] is updated based on the experimental results.

Experimental setup
A prototype of a mesh-based CFHEX has been fabricated based on the numerical analysis [1] and experimental measurements of mesh and wall-to-mesh interface properties [15].The CFHEX consists of two concentric tubes with 330 randomly-oriented stacked copper mesh layers acting as fins to enhance the heat transfer between the two fluid flows.The interface between the tubes and the mesh forms a simple contact: the mesh remains in the position due to dense stacking of the layers and a moderate contact force between the mesh wires and the concentric tubes.Its geometry with the key dimensions is presented in Fig. 1 and the experimental setup constructed to evaluate its performance, namely effectiveness ∊ and pressure drop Δp, for a range of operating conditions and fluids is depicted in Fig. 2.
The test bench presented in Fig. 2 consists of a two-stage Gifford-McMahon (GM) cryocooler 1 and a fluid convection loop that enables the testing of the CFHEX.The two-stage cryocooler is used because in the future the test bench will be extended to form a full prototype of a remote cooling system [1].The operating fluid for the convection loop (e.g.argon, helium, nitrogen, neon) is supplied from a separate gas bottle and circulated using a pump 2 (P 001).The operating fluid, which is pressurised by P 001, warms up.To maintain it at a stable temperature before entering the CFHEX, it is passed through a water heat exchanger.To dampen the oscillations in the fluid (created by the pump), two buffer volumes (Buffer volumes 800 and 900 in Fig. 2) are placed on the highpressure (HP) and the low-pressure (LP) sides of the convection loop.The pressure in different parts of the circuit is regulated by means of the bypass valve (HV700) and Joule-Thomson valve (JT) based on the amount of the gas filled from the bottle to the system.Each section of the circuit that may be subject to overpressure is equipped with a pressure relief device (SV), which is set to an appropriate opening pressure as indicated in Fig. 2. The mass flow rate in the system is regulated and measured by means of a mass flow controller 3 , comprising a mass flow transducer (MFT) and a control valve (CV 800).
The parts of the system that operate below room temperature are mounted in a vacuum chamber (typical pressure during operation: 10 − 7 mbar).To reduce radiation heat loads, most parts in the vacuum chamber are wrapped in multi-layer insulation (MLI) blankets and are additionally protected by a copper thermal shield.The latter is suspended from the top flange of the vacuum chamber.It is thermally decoupled from it using fibreglass composite (G10) pillars and precooled to ≈ 50 K by the first stage of the cryocooler via flexible copper braids.
The low-temperature parts of the fluid loop consist of thin-walled

Symbols α f
Fluid-to-mesh heat transfer coefficient in W/(m 2 K)  To monitor and regulate pressures and temperatures in the system, the setup is equipped with two differential and two absolute pressure sensors (Rosemont and WIKA Tronic), ten temperature sensors (two TVO 4 and eight Pt1005 ) and three polyimide foil heaters.The positions of the most important sensors are indicated in Fig. 2. Absolute pressure sensors are mounted outside of the vacuum chamber, while differential pressures are measured using thin capillaries welded to the inlet and outlet of the high-and low-pressure flow passages.All pressure measurement points are located at least ≈ 10 tube diameters away from the respective upstream geometry changes to ensure uniformity of the fluid flow.
All temperature sensors apart from T4 are mounted on the surface of the fluid loop piping.Indium foil is used to improve thermal contact, and Kapton tape is used for electrical contact insulation.The sensors are pressed to the surfaces with Teflon tape and are covered with MLI, which reduces additional heat inleaks by radiation.The thin stainless steel piping (wall thickness is around 1 mm) at the sensor locations ensures that the difference between the fluid flow and measured temperatures is minimised.Sensor T4 is mounted directly in the flow passage using a leak-tight feedthrough.Heaters EH210, EH220 and EH310 6 , in combination with a temperature controller 7 , are used to regulate the cryocooler stage and flow distributor temperatures.The heater foils are glued on the respective surfaces using cryogenic high-conductivity epoxy glue (Stycast 2850FT).
A four-wire arrangement (two twisted manganin wire pairs) is used to supply the current and measure the voltage of the temperature sensors.A similar arrangement is used for the heaters, however, copper wires are used for the current leads.The length and materials of the heater wiring were adapted such that the self-heating is balanced with the passive heat inleak.The heat inleak by conduction along all wires is intercepted by pre-cooling the wires on the copper thermal shield.
The temperature sensors are powered by two current sources8 (depending on the type of sensor) and the voltage drop is read out using a multimeter 9 .Data are acquired using a custom-written LabVIEW 10program and are post-processed using Python 11 and Matlab12 scripts.

Measurement uncertainty evaluation
Because of the high CHFEX effectiveness values that are reported in this paper for different fluids, we first outline the uncertainty evaluation methods and the strategies used for error reduction in detail.
The mass flow rate and pressure measurement uncertainties were calculated based on the accuracy of the MFT and pressure transducers, one-year multimeter accuracy and the standard deviations of the measurement points during the acquisition period.As an example, some typical measured mass flow rate, absolute and differential pressure values would have the following uncertainties: ṁ = 250±2.75mg/s (helium), ṁ = 1000±8.3mg/s (neon), p hp = 5±0.04mbar, p lp = 1±0.02mbar, p hp = 4±0.2mbar and p lp = 4±1 mbar.The uncertainties in the individual experiments, which will be presented in the following sections, are stated in the captions of the respective figures.Amongst all the instrumentation, the uncertainty of the temperature sensors has the largest impact on the total effectiveness uncertainty.The temperature values that are measured at each end of the CFHEX are relatively close to each other.The effectiveness is determined by tem-Fig.1. Photo of the fabricated CFHEX (left and top right) and flow distributor (bottom right).The CFHEX will be integrated in the remote cooling system [1.] as 'CFHEX 1'.perature differences (see Section 4.3), thus the relative accuracy of the temperature measurements at each CFHEX end is very critical.The experiments are typically performed at large ΔT (e.g.50 K at the cold CFHEX end to 290 K at the warm end).Therefore, two different strategies were employed to cross-calibrate the respective sensors depending on the temperature range of interest to minimise the total effectiveness measurement uncertainty.
Below 70 K, all the relevant sensors (T2, T3, T5 and T6 in Fig. 2) were calibrated against a more accurate reference TVO sensor.This was done by mounting them on the 2 nd stage of the cryocooler, which was then subjected to a stepwise warm-up.The resistance of each Pt100 could then be correlated to the temperature measured by the reference TVO and the dependency could be described by a polynomial fit.The resultant combined measurement uncertainty of T2, T3, T5 and T6 is in this case a sum of Pt100 and reference TVO sensor errors.This includes the uncertainty contributions from the Pt100 polynomial fit, the TVO fit provided by the supplier, the standard deviations of the temperatures that were measured during the tests (containing noise and small drifts) and the sensor resistance errors.The latter were calculated based on the one-year accuracy of the current source powering the sensors and the multimeter used for the voltage readout.As a result, typical absolute temperature errors at 50 K would amount to ±0.2 K for a TVO and ±0.4 K for a Pt100 sensor.However, following the cross-calibration activities, the relative error between two cold end Pt100 sensors at 50 K amounts to ±0.12 K with the rest of the uncertainty coming from the standard deviations of the temperatures during the particular test.
Above 70 K (sensors T1 and T4), the standard Pt100 calibration curves from the supplier were used.To further reduce the error Fig. 2. Schematic of the test stand for the CFHEX performance evaluation.The fluid temperature conditions are ensured by means of a two-stage GM cryocooler, regulated by three electric heaters (EH) and measured with temperature sensors (T1-T6).The fluid is circulated using a compressor pump (P 001), while the mass flow rate is set by a mass flow controller with its respective control valve (MFT + CV 800).The fluid pressure is set with hand (HV) and pressure regulation (PRV) valves, and measured with absolute (PT) and differential (PDT) pressure transducers.
A. Onufrena et al. originating from the sensor current supply and acquisition chain, the sensors were calibrated at 273.15 K.This temperature condition was achieved by submerging the Pt100 sensors in a bath containing a wellestablished mixture of distilled water and ice.The standard Pt100 calibration curves were then adjusted to ensure that the sensor resistance measured during the calibration activity corresponded to 273.15 K.As such, the uncertainty of the current source could be eliminated and the remaining error would come from the standard deviation of the temperature determined throughout the test.Above or below 273.15 K, this error e was assumed to propagate according to e = 0.0017 × (T − 273.15) dependency indicated by the Pt100 supplier.In addition, the uncertainties of a standard Pt100 fit and one-year accuracy of the multimeter were included for the error approximation.A typical absolute error of a Pt100 sensor at 290 K amounts to ±0.14 K.However, based on the sensor cross-calibration activities, the relative error between two warm end Pt100 sensors at 290 K is ±0.04K during a measurement run with the rest of the uncertainty coming from the standard deviations of the temperatures during the given test.
The resulting effectiveness errors that take into account all the aforementioned uncertainties are stated in the captions of the respective figures in the following sections.

Experimental results and numerical model correlation
In this section, an in-depth analysis of the performance of the constructed CFHEX is presented.The analysis is based on the measured pressure drop and the determined effectiveness for the range of operating conditions as well as the total (conduction and radiation) static loss.The CFHEX is designed to operate with the fluid inlet temperatures of ≈290 K and ≈50 K at the warm and cold ends, respectively.The performance results for this nominal temperature range are presented.However, the CFHEX performance is also measured at warm (> 280 K) conditions.The warm pressure drop measurements are performed to propose a better friction factor dependency for the used mesh (see Section 4.1).The warm effectiveness measurements are performed to validate that the correlation factors, which are proposed for the numerical model [1] (see Section 4.3), improve the model predictions across a wide range of operating temperatures.In addition, warm tests allow to evaluate the CFHEXs performance with a variety of fluids (e.g.nitrogen, argon), which would not be possible in the 50 K-290 K temperature range due to a higher boiling point of these fluids.Tests with other gases allow to gain further confidence in the numerical predictions.

Pressure drop
The pressure drop Δp of the CFHEX in the remote cooling system has a direct influence on its maximum cooling power.High Δp in the CFHEX passages results in a lower Δp across the JT valve and a higher operating temperature at the CIF due to higher vapour pressure.Δp is defined as: where f is the Re-dependent friction factor between the fluid and the mesh, A fr is the frontal area faced by the fluid flow, e v and d h are the porosity and the hydraulic diameter of the mesh, respectively, and L is the length of the mesh stack in the direction of the fluid flow.ṁ, ρ and u are the mass flow rate, density and velocity of the fluid passing through the mesh, respectively.For the design and analysis of our CFHEX, the friction factor model from Barron [19] was taken as a baseline [1], namely f = C1 Re (1 +C 2 Re 0.88 ) with parameters C 1 and C 2 for a porosity 0.60 < e v < 0.85.This model was deemed to be the most appropriate as it describes the friction factor measured for a similar type of woven mesh.
The pressure drop across the CFHEX passages was measured to verify whether the developped numerical model is suitable for Δp predictions.
All the presented results are the total Δp values, which are derived by adjusting the measured static pressure drop for the dynamic pressure head in the pipes at the respective measurement locations.Further discussion will cover the experimental Δp results for a wide range of operating mass flow rates and pressures, four operating fluids (helium, neon, argon and nitrogen) at warm (> 280 K) and two operating fluids (helium and neon) at cold (298 K to 46 K) conditions.Generally, three types of data will be presented: the measured Δp, the corresponding predicted Δp calculated using the friction factor from Barron [19] (initial assumption in the model) and the predicted Δp calculated using the experimentally derived f − Re fit 2 from Fig. 5b (which is explained in more detail further in this section).These results will allow to confirm the applicability of the experimentally derived fit 2 and will give an insight on the loss and heat transfer mechanisms in the CFHEX.Fig. 3 depicts the Δp variation with the mass flow rate (system inlet Fig.  1) from which it follows that Δp∝ ṁ2 f for constant pressure and temperature conditions.As ṁ increases, Re will also increase and f will decrease.However, the increase in the ṁ2 term dominates, thus an increase in Δp with ṁ can be observed in Fig. 3. Fig. 4 depicts the Δp hp variation with inlet pressure p hp in the HP fluid flow passage (mass flow rate ṁ is kept constant) for helium, argon and nitrogen at warm conditions.It can be seen that the Δp decreases with p.Under a fixed ṁ condition, it follows from Eq. ( 1) that Δp∝1/ρ (since ṁ, and hence Re and f remain approximately constant).Density varies linearly with pressure for an ideal gas at a constant temperature, which leads to the conclusion that Δp∝1/p.Fig. 4 confirms that the measured Δp hp is inversely proportional to the pressure p hp for different gases.
It can be seen from Fig. 3 and Fig. 4 that the predicted pressure drop (solid lines in the graphs), which is calculated using the friction factor model from Barron [19], gives a higher predicted Δp than the experimental data in all cases.To improve the predictions in accordance with the experimental data, the friction factor can be back-calculated using Eq. ( 1) from the Δp measured at warm conditions.If the friction factor is described as a function of a non-dimensional Re parameter, the obtained f − Re dependency should be applicable to a range of operating conditions, i.e. different gases, temperatures and pressures.
Fig. 5a shows the friction factor f dependency on Re, which was calculated from the numerous pressure drop measurements in warm conditions.It was assumed for the f calculations that the temperature in the CFHEX passage in question is the average between its inlet and outlet.The determined f was found to follow the same trend as the model from Barron [19], but the latter predicts higher values.Fig. 5b shows the experimental friction factor data (blue) from Fig. 5a plotted on logarithmic axes together with other theoretical models and literature data.It can be seen that the experimental values from Koettig [20] for woven mesh closely match the determined f.The determined friction factor was fitted with two functions: • Fit 1: (3.68/Re)⋅(1 + 22.5⋅Re 0.27 ).The general shape of the fit is similar to that suggested by Barron [19]; • Fit 2: 86.2⋅(Re − 0.74 ).The general shape of the fit is similar to that suggested by Vanapalli [21].
As both fits give similar results, the simpler fit 2 was chosen for further Δp predictions.
The pressure drop was then calculated using the numerical model with f − Re fit 2 to verify its applicability.The predictions for the warm tests are plotted as the dashed lines in Fig. 3 and 4. It can be seen that the Δp predictions based on fit 2 are closer to the experimental data.The maximum average deviation of newly predicted Δp from the experimental values is 13 % and it is due to the uncertainty of the experimentally derived fit 2, which was used as a universal model across the entire Re range and for all operating fluids.
The f − Re dependency could not be extracted in a similar way from the cold test data due to large temperature gradients in the CFHEX passages.However, since fit 2 depends on a non-dimensional Re parameter, it is possible to investigate if it remains applicable for Δp predictions at low temperature.The measured Δp at cold conditions together with the Δp based on the fit from Barron [19] and fit 2 are presented in Fig. 6-8.Fig. 6 depicts the Δp hp variation with p hp for helium, Fig. 7 and 8 show the Δp variation with ṁ for helium and neon, respectively.It can be seen that fit 2 improves the Δp predictions significantly for all the cold tests, even though the fit itself is based on the warm test data.The remaining difference between the predicted and measured Δp may suggest that the current numerical model [1] does not yet account for a number of effects, such as lateral flow due to radial temperature gradients in the mesh or imperfect flow distribution.These effects would be particularly pronounced towards lower temperatures.
Moreover, it can be seen from Fig. 7 and 8 that the Δp hp variation with ṁ produces a more curved profile compared to the Δp lp variation.This can be explained by analysing Eq. ( 1) from which it follows that Δp hp ∝ ṁ2 f hp and Δp lp ∝ ṁ2 f lp at a given ṁ (provided that pressure and temperature remain relatively constant throughout the test).The terms ṁ2 and f follow opposite trends: as ṁ increases, so does Re causing a decrease in f [1].As an example, the relative variations of both terms for the helium HP stream at p hp = 2.7 bar and LP stream p lp = 1.4 bar are depicted in Fig. A.17 in Appendix A. In the 50 mg/s-209 mg/s interval, Re hp = 11-46 and Re lp = 4-16 ranges are observed.This implies that f decreases only slightly for the high-pressure and significantly for the low-pressure stream in this mass flow rate interval.As a result, the behaviour of Δp hp is dominated by the ṁ2 rather than by the f hp term.
Hence, the Δp hp versus ṁ profile has a more curved quadratic shape than the Δp lp versus ṁ profile.
Overall, it can be concluded that the Δp, which was calculated using the experimental f − Re fit 2, is lower than the Δp, which was calculated using the f − Re model from Barron [19].This may suggest that there is less interaction between the fluid and the mesh, hence the fluid-to-mesh heat transfer coefficient would also be lower than in the assumed model from Barron [19].This is in line with the measured effectiveness results, which are presented and discussed in Section 4.3.

Static loss
Axial conduction is an important loss mechanism in higheffectiveness compact CFHEXs [19], thus the static loss measurements are a powerful tool in the understanding of the heat exchanger performance.An experimental evaluation of the total static loss for our design would allow to confirm that the stacked mesh maintains its low axial thermal conductivity [15] once it has been integrated in the CFHEX.The measured static loss value can be then used to adjust the temperaturedependent parameters of the simulation (e.g.thermal contact between the mesh layers) to improve the numerical predictions of CFHEX effectiveness.
The method outlined by Waldauf et al. [22] was used to perform the static loss measurement.A great advantage of this method is that it allows to determine a total static loss of an assembly for a given set of temperature conditions without knowing the exact thermal conductivity and heat capacity of its individual components as well as thermal conductance of numerous contacts in the complex system.
The measurements were performed in the following way: the CFHEX was pre-cooled to its operating temperature using the setup shown in Fig. 2 and then thermally decoupled from the cooling source by elimination of fluid from the circulation loop.Further, a known heat load P was applied at the bottom of the CFHEX using EH310 and the warm-up time Δτ for T6 to reach a defined temperature was recorded.The heating powers P could then be plotted versus the inverse warm-up times 1/Δτ as shown in Fig. 9.The intersection of the constant-temperature lines with the vertical axis corresponds to the amount of heat that would need to be extracted from the system after an infinite time to keep it in thermal equilibrium, which is equal to the total static loss by Fig. 5. Variation of friction factor with Reynolds number for different gases at warm conditions.Points and lines represent the experimental and simulation data, respectively.(a) Experimental data measured for helium, neon, argon and nitrogen gases compared to the dependency from Barron [19] used in initial simulations.(b) Experimental data from (a) plotted on logarithmic axes and compared to the stated literature dependencies [20,19] as well as custom-made fits based on the shapes from Barron [19] and Vanapalli [21].The proposed fits 1 and 2 overlap; the standard deviation of the fits. is ±0.78.Fig. 6.Variation of pressure drop with inlet pressure for different helium gas pressures at cold conditions.Points and lines represent the experimental and simulation data, respectively.The source of the friction factor used is indicated in brackets.T hp,in lies between 294 K and 297 K and T hp,out lies between 66 K and 77 K during the tests.The maximum Δp hp , p hp,in and ṁ measurement uncertainties are ±0.23 mbar, ±14 mbar and ±2 mg/s, respectively.conduction.The test was performed to estimate the conduction and radiation static heat load to 60 K from the 293 K warm end of the CFHEX.An additional test was carried out with static helium present in the circulation loop, which allowed to estimate the contribution of conduction through helium gas to the static heat loss.The interested reader is directed to the original source [22] where the method of residual heat load determination of non-uniform assemblies is discussed in more detail.
In the 60 K-293 K temperature range, a total static loss of 5.5±0.3W can be estimated from the intersection of the constant temperature lines with the y-axis in Fig. 9.The ±0.3 W error includes both the measurement error, uncertainties of the line fits in Fig. 9 and small temperature drifts.For the nominal operating point of the system, approximately 210 W of heat are transferred from HP to LP flow (will be discussed in Section 5.1).Therefore, the static loss of 5.5±0.3W amounts to 2.6±0.1 % of the total heat transfer, which contributes to ineffectiveness of the CFHEX along with the other factors such as thermal resistance between the flows.This suggests that the overall influence of this error on the predicted effectiveness at these conditions in Fig. 10-16 will be below 0.1 %.
The static loss of 5.5±0.3W amounts to 2%-14% of the overall heat transfer between the CFHEX fluid flows in the 50 mg/s-250 mg/s mass flow rate range (see Table 1).The reduction in the static loss would allow more heat to be transferred between the flows and the resultant CFHEX effectiveness would increase further.Hence, a deeper assessment of static loss contributors can prove to be useful.
The contributions of the individual components to the total value are summarised in Table 1.The total static loss of 5.5 W originates from the   A. Onufrena et al. axial conduction through the CFHEX walls and across the mesh layers as well as from thermal radiation.The contributions of helium, the inner and outer tubes were approximated from the known fluid and material properties; the radiation heat load was approximated based on the CFHEX geometry, mounting arrangement and the number of MLI layers in the setup.The rest of the static loss must originate from the axial conduction through the mesh amounting to 1.8 W based on the 5.5 W total static loss.However, a heat load of 0.14 W was calculated assuming the experimentally measured mesh axial conductivity under 2.25 kPa compression [15].It was shown in these earlier studies that the axial conductivity of the mesh increases with the compression force between its layers.Thus, the higher thermal conduction, which was estimated during our static loss measurement, suggests that the mesh was overcompressed during the CFHEX assembly.The 330-layer uncompressed mesh stack should have a total height of 207.9 mm.The actual mesh stack height in the CFHEX is 170 mm (see Fig. 3a), which corresponds to a compression force above 2.25 kPa based on the stress-strain profile presented in [15].
To improve the numerical predictions, the axial thermal conductivity of the mesh used in the numerical model [1] was adjusted such that the contribution of the mesh is consistent with the experimentally derived value of 1.8 W. The variation of the predicted effectiveness with the helium mass flow rate based on the initial axial thermal conductivity of the mesh as well as the one derived from the static loss tests are depicted in Fig. 10.It can be seen that the maximum predicted effectiveness decreases from 96.5 % to 92.7 % when a higher axial conduction through the mesh is introduced.Even though a 3.8 % decrease on predicted effectiveness is observed, an increased compression between the mesh layers is expected to lead to a stronger contact force between the mesh wires and the inner and outer CFHEX tubes.This implies that the meshto-wall contact conductance coefficient α IF is also expected to be larger than the experimental values that were measured initially [15] as the thermal contact conductance between two materials has been shown to increase with the contact force [23].This will have further implications on the effectiveness values discussed in the following Section 4.3.

Effectiveness
The CFHEX effectiveness is the most important parameter that for a large part will define the performance of the entire remote cooling system.Hence, the main focus of the experimental campaign was to characterise it for a range of conditions and gain insight into the origin of the differences between the experimental and numerical results [1].This would allow to further improve the model predictions and identify the main improvement areas for future CFHEX designs.
The effectiveness is defined as the ratio between an actual heat transfer rate and the thermodynamically limited maximum possible rate.If the mass flow rate is the same for both fluid streams, the effectiveness ∊ can be expressed using the enthalpy approach following [19]: depending on the stream used.In Eqs. ( 2) and (3), h denotes the specific enthalpy of the HP or LP flow calculated at the pressure indicated by the subscript and at the temperature stated in the brackets.Here, referring to Fig. 2, T hp,in is T 1 , T hp,out is T 2 , T lp,in is T 3 , and T lp,out is T 4 .In theory, ∊ hp and ∊ lp should be equal.However, the CFHEX is not perfectly insulated during the tests, hence heat is transferred between the CFHEX and the surroundings.Moreover, heat is conducted along the CFHEX (mainly the residual heat leak), which leads to a difference in effectiveness values depending on the stream used.Fortunately, the average value ∊ avg = (∊ hp +∊ lp )/2 is insensitive to the heat transfer between the CFHEX and the surroundings, hence provides a good representation of the CFHEX performance [24].The effectiveness values ∊ avg , ∊ hp and ∊ lp can be deduced experimentally by measuring the fluid flow inlet and outlet temperatures (T1, T2, T3 and T4 in Fig. 2) and pressures (PT1 and PT2 in Fig. 2), for a range of operating conditions.The test parameters used in the experimental campaign are summarised in Table 2.The numerical predictions [1] (further confirmed experimentally) suggest that the effectiveness is not largely affected by changes in pressure conditions, while it is significantly affected by the fluid mass flow rate.Hence, the fluid stream pressures were kept constant in the tests presented in Table 2 and the mass flow rate was varied.

Warm tests
The variation of effectiveness with mass flow rate measured at warm conditions (test 1 (He) in Table 2) is shown in Fig. 11a together with the numerical predictions.The numerical simulation assumes an increased axial conductivity of the mesh, which was adjusted based on the static loss analysis outlined in Section 4.2.The parts of the experimental setup  between the ends of the CFHEX and the temperature measurement locations are modelled as hollow tube-in-tube HEX extensions of appropriate dimensions.
Overall, the numerical predictions in Fig. 11a show a good agreement with the experimental data.A larger spread between the experimental ∊ hp and ∊ lp values is observed if compared to the spread between the predicted ∊ hp and ∊ lp especially at low ṁ.This can be explained by the presence of the residual heat transfer to the CFHEX, which is not considered in the simulation.This heat inleak results in an increase in the temperature of the returning flow, leading to a higher ∊ lp and a lower ∊ hp .As mentioned previously, the average effectiveness values should not be sensitive to this effect.
The predicted ∊ avg trend is in good agreement with the experimental data with slightly lower values predicted towards higher ṁ.This suggests that the thermal conductance in radial direction between the two CFHEX streams is higher than anticipated.The radial conductance comprises four contributions, which are depicted in Fig. 12: the convective heat transfer between the mesh and the fluid (function of the fluid-to-mesh heat transfer coefficient α f ), the radial conduction through the mesh (function of the radial conductivity of the mesh), the mesh-towall contact conductance (function of the mesh-to-wall contact conductance coefficient α IF ) and thermal conduction through the inner tube in radial direction [1] (function of the bronze conductivity).Some of these four contributions have likely been underestimated during the numerical analysis.An assessment of each individual contribution led to the following observations: 1. Radial conduction through the bronze inner tube and through the mesh is well defined (the radial conductivity of the mesh was measured experimentally [15]).
2. The fluid-to-mesh heat transfer coefficient α f was computed based on the data from Barron [19] that were measured for a woven mesh.However, differences between the literature values and our mesh are plausible as the exact mesh geometry used by Barron [19] is not known.The results in Fig. 5 suggest that the friction factor estimated from the measured pressure drop is lower than the corresponding value from Barron [19].This may indicate that the mesh used in the current CFHEX design exhibits a lower degree of interaction with the fluid than the mesh described by Barron [19].Following this argument, a lower α f value (compared to the α f calculated based on the heat tranfer data from Barron) can be expected for the designed CFHEX.In addition, the numerical model used for predictions does not consider radial temperature gradients within the mesh layers.These can cause undesired radial flow effects that eventually lead to an incomplete heat transfer between the mesh and the fluid.All this suggests that the α f value in the numerical model is overestimated.
3. It was concluded from the static loss measurements (outlined in Section 4.2) that the compression between the mesh layers in the   fabricated CFHEX is higher than initially assumed.This was confirmed via a comparison of the height of a 20-layer mesh stack in the fabricated CFHEX with an equal stack height under 2.25 kPa compression load in a traction machine.The compression stress in the fabricated CFHEX was found to be approximately an order of magnitude higher based on the mesh stress-strain profile [15].This will in turn lead to an increase in the mesh-to-wall contact force, thus improving mesh-to-wall contact conductance [23].Hence, the coefficient α IF is expected to be higher than the initially assumed experimental value from [15].
Based on this assessment, α f is likely to be lower and α IF to be higher than the assumed values in the numerical model.The evolution of ∊ avg predictions based upon the scaling of these two parameters by different factors is shown in Fig. 11b.The two pairs of α f and α IF correlation parameters are shown in Fig. 11b to demonstrate their relative effect on the simulated effectiveness.It can be seen that a proposed 20 % decrease in α f (i.e.0.8α f ) and doubling of α IF result in a better representation of the experimental data.The factor of two increase in α IF is coherent with the adjustment factors suggested in the prior numerical studies [1].
To confirm that the improvement of the predicted results is reproducible, the effectiveness was measured at warm conditions using a different fluid, namely nitrogen (test 5 (N 2 ) in Table 2).Even though the peak effectiveness of the CFHEX (with nitrogen as an operating fluid) is predicted to occur at a higher ṁ (above 500 mg/s) compared to the helium case, it lies within a similar range of volumetric flow rates V. Hence, the CFHEX performance with the two gases can be compared by assessing the effectiveness variation with V in normal litres per second, which is presented in Fig. 13.The aforementioned α f and α IF correlation factors are assumed for the ∊ avg simulation shown in the plot.It can be seen that the suggested decreased α f and increased α IF improve the predicted effectiveness in the nitrogen test as well.

Cold tests
The CFHEX performance was measured at cold conditions (tests 3 (He) and 4 (He) from Table 2) as this is its main temperature range of application, and for further confirmation of the correlation factors.The comparison of ∊ avg values for cold and warm (test 1 (He)) conditions as well as the numerical and correlated curves are presented in Fig. 14.It can be seen that in the cold tests a maximum effectiveness of 94.9 % at ≈ Fig. 12. Schematic of the radial thermal conductance components in the CFHEX with a detail of the inner wall region.Comparison of average effectiveness variation with mass flow rate for helium gas at warm and cold conditions.Points and lines present the experimental and simulation data, respectively.Test 1 (He) is performed at warm conditions, whereas tests 3 (He) and 4 (He) are performed at cold conditions.The maximum effectiveness of 94.9 % is achieved under the cold conditions.The numerical simulation for test 3 (He) is not depicted for clarity as the prediction is very close to that of test 4 (He).Error bars are not shown for clarity (can be found in Fig. 11a and 15).The lines depict the simulation curves with the same simulation parameters as in Fig. 11b and 13 for both warm.and cold cases.175 mg/s (NTU = 18.6) is achieved.Moreover, both the predicted and experimental effectiveness values of the CFHEX are higher at cold test conditions when compared to warm conditions.This is likely the consequence of an increased radial and decreased axial thermal conductivity of the copper mesh [15] as well as a decreased pressure drop when compared to the warm case.The correlation factors applied to α f and α IF improve the predictions in both cases.Moreover, it can be seen that the measured effectiveness at low mass flow rates is higher in test run 4 (He) than in run 3 (He).Even though both tests were performed in similar temperature and pressure conditions, for test 4 (He) the measurement setup was equipped with an improved LP flow distributor (see Table 2 for more information and the version used in each particular test).A better LP inlet flow distribution in test 4 (He) led to a more uniform circumferential heat transfer between the flow and the mesh, which is especially pronounced at lower mass flow rates.As the mass flow increases, the LP inlet flow in the flow distributor becomes more turbulent irrespective of the version used, hence the heat transfer and the effectiveness increase in the CFHEX for both tests.The numerical model considers a well-distributed flow throughout the CFHEX, as such the experimental conditions of test 4 (He) are more in line with the assumptions of the model and the predictions are more accurate.This observation highlights the importance of flow uniformity for the CFHEX performance.Hence, the appropriate design adjustments are foreseen for future setup upgrades.
In the final series of tests, the CFHEX was tested with neon and helium under cold conditions.Even though helium is of main interest for the remote cooling system [1], the characterisation of the CFHEX with neon provides valuable data for future RTB recuperator designs used in space applications [8].The effectiveness results, together with uncorrelated and correlated numerical predictions, are shown in Fig. 15.A maximum effectiveness of 94.5 % was achieved for neon, corresponding to NTU = 17.2, which demonstrates that the high performance of the mesh-based design is maintained for a different fluid.Interestingly, the maximum performance for both gases is achieved at a similar volumetric flow rate of ≈ 1 1 n /s with approximately 210 W transferred heat between the flows.Such a close performance for the two fluids suggests that the internal heat transfer mechanism between the gas and the structure is the same, provided that the gas can be considered ideal.

CFHEX performance overview
The mesh-based inner geometry was identified as the most promising candidate for effective and compact CFHEXs.However, there exists a number of other highly performant solutions.As an example, an effectiveness of 98.1 % with argon in the 0 • C-100 • C range is reported for a recuperator with microchannel-in-shell inner geometry, which is accomplished by Mezzo Technologies for Reverse Turbo-Brayton applications [24].Such an experimental performance makes it one of the most compact and effective amongst the existing heat exchangers.To compare the mesh-based and microchannel-in-shell geometries, the correlated numerical model [1] was used to size a mesh-based CFHEX with 98.1 % effectiveness for operation with argon in the 0 • C-100 • C range and in the conditions reported in [24].The performance parameters of the sized design are presented in Table 3.It can be seen that roughly 15 % of the mass and 70 % of the volume reduction can be achieved with the mesh-based geometry, which makes it a very promising solution for space applications [4,5,8,10,12].
The CFHEX performance is determined by a complex parameter field, which includes CFHEX geometry and materials, the fluid type and flow regime as well as the mass flow rate, pressure and temperature conditions.The latter are typically defined at system level and are inputs for the CFHEX design.However, a variety of operating conditions may be of interest depending on the system in question.For that reason, an assessment of the sensitivity of the CFHEX performance to a simultaneous change in various operating conditions is required.This would allow us to evaluate the impact of the CFHEX on the global system performance, to identify the appropriate directions for the future CFHEX designs as well as to confirm the reliability of our numerical model [1].
The performance of the remote cooling system from [1] is primarily determined by the mass flow rate and the inlet pressure of the fluid flow.Therefore, the fabricated CFHEX was tested across an appropriate range of helium ṁ and p hp under warm and cold conditions.
The experimental results are depicted in Fig. 16 together with the simulation planes.It can be seen that the pressure drop is affected by both ṁ and p hp , whereas the effectiveness is primarily dependent on ṁ rather than p hp in the 1 bar-5 bar range.This observation can be explained by analysing the dependency of the convective heat transfer on the fluid pressure.
The fluid-to-mesh convective heat transfer coefficient α f is expressed as [1,19]: where c p is the specific heat capacity of the fluid, e v A fr is the free-flow Fig. 15.Comparison of average effectiveness variation with normal volumetric flow rate for helium and neon at cold testing conditions.The points represent the experimental data.The lines depict the ∊ avg simulation curves with the same simulation parameters as in Fig. 11b, 13 and 14.Black and green data correspond to helium and neon results, respectively.Error bars are shown only for the average effectiveness data for clarity.The maximum average effectiveness of 94.9 % is achieved in test 4 (He) and 94.5 %. in test 6 (Ne).

Table 3
Performance comparison of a mesh-based CFHEX with microchannel-in-shell recuperator from Mezzo Technologies [24].being fluid viscosity and thermal conductivity, respectively.j H is the Colburn J-factor, which represents the heat transfer capabilities and is a function of the Reynolds number Re = ρud h /μ that is defined with the fluid density ρ, velocity u and respective hydraulic diameter d h [14,19].

Mesh-based CFHEX
Colburn suggested that this dimensionless factor (which can also be expressed as j H = StPr 2/3 ) can be correlated with the Re number.Nowadays, this dependency is widely used in heat transfer analysis [25].
The increase in pressure causes an increase in density for an ideal gas at a given mass flow rate and temperature.However, if ṁ = ρuA fr e v is fixed, the product ρu remains unchanged irrespective of the changes in pressure.This in turn implies that the Reynolds number Re = ρud h /μ is approximately constant for the range of the tested pressures as the viscosity μ does not experience a significant change in the 1 bar-5 bar range.Based on this, the Re-dependent Colburn J-factor also remains unchanged with pressure along with the other terms in Eq. ( 4) provided that the mass flow rate and the temperature are kept constant.As a result, the fluid-to-mesh heat transfer coefficient α f and the effectiveness remain constant with varying pressure.The observed low sensitivity of the CFHEX effectiveness to the fluid flow pressure suggests that the designed CFHEX can maintain its high performance for a wider range of operating pressure conditions.This behaviour opens more options for remote cooling system designs [1] and, therefore, helps to meet a greater variety of cooling needs.
The simulation planes depicted in Fig. 16 use the 0.8α f and 2α IF adjustment factors that originate from the numerical model correlation, which was presented earlier.These correlation parameters are coherent with the observations outlined in Section 4.3.1 (e.g.reduced or incomplete heat transfer and increased mesh-to-wall contact conductance) and, as evident from Fig. 16, are in a good agreement with the experimental data across a wide range of operating conditions.

Remote cooling system performance
The fabricated mesh-based CFHEX will be integrated in the remote cooling system prototype [1] as 'CFHEX 1'.Helium will be used as the operating fluid in the system with inlet and outlet pressures of 5.3 bar and 1 bar, respectively.Table 4 summarises the main CFHEX performance parameters during test 4 (He) from Table 2 together with its performance predicted by the correlated numerical model at the nominal remote system operating conditions.The resulting power at the remote cooling interface (CIF) was calculated for two mass flow rates: ) and 180 mg/s ( ṁ corresponding to the maximum measured CFHEX effectiveness of 94.9 %).The calculated power values suggest that a better performance is achieved for the increased ṁ = 180 mg/s, hence the nominal operating mass flow rate of the system was adapted accordingly.A pressure drop of 15 mbar (combined value for both streams) was derived based on the experimental data for these conditions.This value is significantly lower than the initially assumed 100 mbar per stream [1].
The experimentally derived effectiveness and pressure drop of the CFHEX suggest that the remote cooling system should be able to achieve 0.9 W at the 4.5 K remote CIF with the original cooling source, which provides 0.8 W at 9 K, if all three CFHEXs maintain the current performance.Since the static losses are expected to be reduced for CFHEXs 2 and 3 due to a decreased axial thermal conductivity of the materials at lower temperatures, an even higher cooling power at the CIF is likely to be achieved.These findings suggest that the addition of the fluid circulation loop with a JT-expansion and three highly effective CFHEXs can significantly improve the performance of the original cooling source.

Improvements and future work
A high maximum effectiveness of 94.9 % corresponding to an NTU of 18.6 has been experimentally achieved with the constructed compact mesh-based CFHEX.However, it can be seen from Table 4 that this value is slightly below the initially predicted 96.5 % [1].The small difference can be associated with a number of factors: a higher measured static heat loss due to over-compression of the mesh, an uneven flow distribution and incomplete heat transfer between the flow and the mesh due to radial temperature gradients that lead to undesired flow effects.
The effect of the static loss can be further analysed by assessing the percentage of the total heat transfer between the two flows.It can be seen from Table 1 that the static loss comprises an approximately equal part of the total heat transfer between the flows for both warm and cold conditions.However, it comprises a larger proportion of the total heat transfer at low mass flow rates, hence it has a more pronounced negative effect on the CFHEX effectiveness in these operating conditions.
The main contributors to the static loss are the inner and outer tubes as well as the mesh as seen from Table 1.A number of modifications are planned for the current design to further reduce the static loss and improve the effectiveness.Thinner inner and outer tubes are considered: manufacturing attempts have shown that a 0.2 mm tube thickness can be achieved for a structurally sound design.The outer tube is not required to transfer heat well in radial direction, hence insulating glass fibre composites can serve as an alternative to the current stainless steel tube.However, this choice of materials will inevitably lead to a difference in thermal dilatation of the materials, thus adding complexity to the setup.
It was suggested in Section 4.3 that a higher compression force between the mesh layers results in a stronger mesh-to-wall contact, which leads to an increased effectiveness towards higher flow rates.However, a higher maximum effectiveness could be achieved if the compression was maintained at 2.25 kPa (the value used for the initial predictions in [1] depicted in Fig. 10) or below.As a result, special care will be taken to maintain a lower compression force between the mesh layers during the CFHEX assembly to further reduce the axial conduction in the future designs.In addition, alternating layers of a less conductive mesh (e.g.stainless steel or plastic mesh) can be introduced.These would allow the creation of poorly conducting mesh-to-mesh interfaces, thus decreasing the effective axial conductivity of the mesh.Theoretical calculations show that placing 30 equispaced layers of stainless steel mesh along the 330 copper mesh stack allows for a threefold reduction in the original axial conduction through the mesh stated in Table 1.As a further optimisation, the spacing between the less conductive mesh layers should gradually decrease towards the warmer and more conducting CFHEX end.It is also worth mentioning that the axial thermal conductivity of the chosen tube and mesh materials decreases at lower temperatures.This, combined with an increased radial conductivity of the mesh towards lower temperatures [15], will allow for an even higher effectiveness of the colder CFHEXs in the remote cooling system [1].
As outlined in Section 4.3.2, the flow distribution at the flow inlets has a significant impact on the effectiveness, especially at low mass flow rates.Thus, improved flow straighteners are considered for the future designs at the respective locations.Moreover, the measurement results suggest that the fluid-to-mesh heat transfer coefficient α f might have been overestimated in the predictions.This can be due to the differences between our CFHEX and the experimental data presented in the literature [19,20,26] in terms of the used mesh geometries and stacking.An experimental measurement of the fluid-to-mesh heat transfer is planned to confirm this.
Another important factor that leads to an increase in CFHEX effectiveness is a high inner wall-to-mesh contact conductance [1].The latter can be achieved via a higher mesh-to-wall contact force [15,23].Alternatively, different manufacturing techniques can be considered to increase the contact conductance, such as sintering of the mesh to the inner tube or brazing it via a deposition of a thin layer of a brazing agent.Such a layer would likely have a high axial thermal conductivity, hence it will increase the total static loss.However, a calculation has shown that the CFHEX effectiveness deterioration due to a static loss introduced by deposition of a 10-micron thick layer of silver brazing agent would be negligible compared to the effectiveness enhancement that can be achieved.3D printing and additive manufacturing techniques can allow for further performance improvement and will be studied for future designs.

Conclusions
Compact high-effectiveness mesh-based CFHEXs have a great potential to enable a variety of on-ground and space applications.For a cryocooler-based remote cooling system [1], a high-effectiveness meshbased CFHEX was constructed.The experimental performance of this CFHEX in the 46 K-307 K range was presented and compared to the initial numerical predictions [1].A high effectiveness value of 94.9 % was achieved (NTU = 18.6) with helium as a working fluid demonstrating a combined pressure drop of ≈ 15 mbar (with only 7.9 mbar for the LP flow) at the nominal remote cooling system operating conditions.In addition, a maximum effectiveness of 94.5 % (NTU = 17.2) was reached for neon as an operating fluid in the 51 K-290 K range.That performance was achieved by a compact (only 170 mm-long) design.

Table 4
Summary of the main performance parameters of the CFHEX at test 4 (He) conditions from Table 2 and at nominal operating conditions of the remote cooling system [1].The latter is predicted by the correlated model with 0.8α f and 2α IF .Nominal operating conditions of the system: ṁ = 180 mg/s (adapted), p hp,in = 5.3 bar, p lp,out = 1.0 bar.

Cold conditions Remote cooling system conditions
Test: 4 (He) (values are predicted with correlated model) Maximum ∊avg 94.9 % at 180 mg/s 94.8 % at 150 mg/s (initially stated ṁ [1]) 94.9 % at 180 mg/s (adapted ṁ With the demonstrated effectiveness, the mesh-based CFHEXs integrated in a remote cooling system [1] can strongly enhance the cooling power of a standard GM-cryocooler (e.g.≈ 0.8 W at 9 K) such that it provides a similar cooling power at 4.5 K.It suggests that mesh-based CFHEXs can serve as a promising future design choice for remote cooling systems and space RTB neon recuperator applications.
The differences between the experimental findings and the initial numerical predictions were analysed.It was found that a slightly lower effectiveness was measured due to an increased axial conduction in the CFHEX.This was confirmed by the experimental measurement of 5.5 W static loss whereas a 3.6 W loss was initially predicted.This increase was attributed to an excessive compression between the mesh layers, leading to a higher axial thermal conductivity of the mesh.The larger compression has also increased the mesh-to-wall contact conductance that helped to achieve a higher effectiveness at higher mass flow rates.However, despite this improvement, the simulation and the experimental data suggest that an overall effect of the excessive compression is detrimental and leads to a lower achieved effectiveness.
The friction factor for the woven mesh was calculated from the measured pressure drop and compared to the numerical models from literature.The experimentally derived friction factor has been found to be lower than the numerical predictions.A new Re-dependent friction factor model has been proposed.
It became evident throughout the test campaign that the flow distribution can have a strong impact on the CFHEX performance and may lead to an incomplete heat transfer between the fluid and the mesh.Additionally, radial temperature gradients in the CFHEX might lead to similar consequences.Further tests are required to better understand these phenomena.
A number of improvements have been suggested for the future CFHEX designs.These include the introduction of layers of a less conductive material for the static loss reduction, geometry changes and the use of novel manufacturing techniques.All these modifications should allow to achieve an even higher CFHEX effectiveness and remote cooling system performance.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
stainless steel tubes to limit the thermal conduction along the fluid flow passage walls.A thermal interface to the first stage of the cryocooler is accomplished via a 2.4 m spiral copper tube HEX.A stainless steel flow distributor (see Fig.1) was designed to guide the fluid flow that is entering and exiting the concentric CFHEX geometry.Besides splitting high-and low-pressure streams, the flow distributor helps to homogenize the returning low-pressure flow before it enters the cold end of the CFHEX by means of eight holes located on the outer ring as shown in Fig.1.

Fig. 4 .
Fig. 4. Variation of HP pressure drop with inlet pressure for different gas pressure at warm conditions.Points and lines represent the experimental and simulation data, respectively.The source of the friction factor used is indicated in brackets.(a) Helium test; CFHEX end temperatures lie between 291 K and 313 K. (b) Argon test; CFHEX end temperatures lie between 294 K and 313 K. (c) Nitrogen test; CFHEX end temperatures lie between 300 K and 313 K.The maximum Δp hp and p hp,in measurement uncertainties in the tests are ±0.23 mbar and ±14 mbar, respectively; the maximum ṁ uncertainties are ±2 mg/s for helium and ±8 mg/s for argon and nitrogen tests.

Fig. 7 .
Fig. 7. Variation of pressure drop with mass flow rate for different helium pressures at cold conditions.Points and lines represent the experimental and simulation data, respectively.The source of the friction factor used is indicated in brackets.The CFHEX warm end temperatures lie between 290 K and 298 K, and the cold end temperatures lie between 46 K and 56 K during both tests.(a) High-pressure stream; the maximum Δp hp and p hp measurement uncertainties are ±0.23 mbar and ±80 mbar, respectively.(b) Low-pressure stream; the maximum Δp lp and p lp measurement uncertainties are ±1.03mbar and ±43 mbar, respectively.The uncertainty of ṁ measurement is ±3 mg/s in both tests.

Fig. 8 .
Fig. 8. Variation of pressure drop with mass flow rate for different neon gas pressures at cold conditions.Points and lines represent the experimental and simulation data, respectively.The source of the friction factor used is indicated in brackets.T hp,in ≈ 291 K and T lp,in ≈ 51 K during the test.The maximum Δp hp , Δp lp , p and ṁ measurement uncertainties are ±0.23 mbar, ±1.05 mbar, ±54 mbar and ±8.3 mg/s, respectively.

Fig. 9 .
Fig. 9. Measurement of the static loss with CFHEX warm and cold ends at 293 K and 60 K, respectively, at the start of the measurement.The intersection of the constant temperature lines with the y-axis indicate the total amount of static heat loss.The maximum power measurement uncertainty is ±7 mW.The total uncertainty on the resultant determined static loss of 5.5 W is ±0.3 W.

Fig. 10 .
Fig. 10.Variation of effectiveness with helium mass flow rate at cold conditions based on two values of axial conduction through the mesh.The maximum predicted effectiveness is indicated for both cases.The simulation parameters are: p hp = 5.3 bar, p lp = 1.0 bar, T hp = 290 K, T lp = 50 K.

Fig. 1 .
** Flow distributor A was upgraded to version B with an improved performance.The top view presented in Fig.1is identical for both versions.However, in version B an additional metal grid is placed before the flow enters the flow distributor to generate turbulence and ensure better homogeneity of the fluid stream.

Fig. 11 .
Fig. 11.Variation of effectiveness with helium mass flow rate at warm conditions.Points and lines represent the experimental and simulation data, respectively.(a) The three curves represent ∊ hp , ∊ lp and ∊ avg as stated compared to the original simulation.(b) The experimental data from (a) with three simulation curves for ∊ avg : the original simulation is compared to the two simulations in which the parameters α f and α IF are altered as stated.The error bars are the same as in plot (a).The maximum uncertainty of the ṁ measurement is ±3 mg/s.

Fig. 13 .
Fig. 13.Variation of effectiveness with normal volumetric flow rate for nitrogen and helium at warm conditions.Points and lines represent the experimental and simulation data, respectively.Error bars are shown only for the average effectiveness data for clarity.The lines depict the ∊ avg simulation curves with the same simulation parameters as in Fig. 11b for the nitrogen a.nd helium tests.

Fig. 14 .
Fig. 14.Comparison of average effectiveness variation with mass flow rate for helium gas at warm and cold conditions.Points and lines present the experimental and simulation data, respectively.Test 1 (He) is performed at warm conditions, whereas tests 3 (He) and 4 (He) are performed at cold conditions.The maximum effectiveness of 94.9 % is achieved under the cold conditions.The numerical simulation for test 3 (He) is not depicted for clarity as the prediction is very close to that of test 4 (He).Error bars are not shown for clarity (can be found in Fig.11a and 15).The lines depict the simulation curves with the same simulation parameters as in Fig.11band 13 for both warm.and cold cases.

A
.Onufrena et al.

3 A
V = 1 l/s V = 1.48 l/s V = 1.48 l/s conditions p hp = 1.7 bar p hp = 1.0 bar p hp = 1.0 bar p lp = 1.4 bar p lp = 1.0 bar p lp = 1.0 bar Tin = 48 K-290 K Tin = 273 K-373 K Tin = 273 K-373 K .Onufrena et al. area faced by the fluid, Pr = c p μ/k is the Prandtl number, with μ and k

Fig. 16 .
Fig. 16.Plots showing the variation of the CFHEX performance parameters for a range of helium inlet pressures and mass flow rates.(a) HP flow pressure drop at warm conditions; (b) HP flow pressure drop at cold conditions; (c) Effectiveness at warm conditions; (d) Effectiveness at cold conditions.The points and the surface maps present the experimental and correlated simulation results, respectively.The simulations assume 0.8α f , 2α IF and experimentally derived friction factor f.
outlet pressures p hp and p lp are kept constant) for helium and neon at warm conditions.Both Δp hp and Δp lp profiles are shown in the figure, thus it should be noted that the cross-sectional areas of the HP and LP passages are different.It can be seen that Δp increases with ṁ.To explain this, one can analyse Eq. ( [19]ariation of pressure drop with mass flow rate for different gas pressures at warm conditions.Points represent the experimental data; solid and dashed lines represent the simulation results based on f from Barron[19]and experimentally determined f (further explained in Section 4.1), respectively.(a)Heliumtest.Two different HP conditions (2.7 bar and 4.0 bar) were tested; CFHEX end temperatures lie between 296 K and 315 K.The maximum ṁ, p, Δp hp and Δp lp measurement uncertainties are ±3 mg/s, ±95 mbar, ±0.23 mbar and ±1.05 mbar, respectively.(b)Neontest; CFHEX end temperatures lie between 289 K and 290 K.The maximum ṁ, p, Δp hp and Δp lp measurement uncertainties are ±5 mg/s, ±74 mbar, ±0.23 mbar and ±1.05 mbar, respectively.A. Onufrena et al.and

Table 1
Relative contributions of different CFHEX components to the total static loss for cold (60 K-293 K, measured) conditions.

Table 2
Test parameters used in the experimental campaign to characterise the CFHEX effectiveness.
* Flow distributor as depicted in